I am trying to find the maximum value of $\lambda$, where 0 $\le$ $\lambda$ $\le$ 90$^\circ$ In the following system of equations $\lambda$, E, $\phi$ are my variables and rest all are arbitrary constants.
Following variables are defined for the sake of simplifying the main equations
$$x = a \cos(E) cos\Omega + a \sin(E) sin\Omega$$
$$y = - a \cos(E) \sin(\Omega) \cos(I) + a \sin(E) \cos\Omega \cos(I)$$
$$z = [N (1 - e^2) + h] \sin\lambda$$
The system of equations are as follows:
$$(N + h) \cos\lambda\cos\phi = x \cos\theta_0 + y \sin\theta_0$$
$$(N + h) \cos\lambda \sin\phi = -x \sin\theta_0 + y \cos\theta_0$$
$$y D \cos\epsilon + z D \sin\epsilon - a^2\ge a \cos\theta\sqrt{a^2 + D^2 - 2D(y\cos\epsilon +z\sin\epsilon)}$$